where the function \(f: \mathbb {R}^n \rightarrow \mathbb {R}\)  has block coordinate-wise Lipschitz gradient and \(\psi : \mathbb {R}^n \rightarrow {\mathbb {R}}\)  is differentiable function (both terms are possibly nonseparable and nonconvex). Optimization problems having this composite structure arise in many applications such as distributed control, signal processing, truss topology design, machine learning, traffic equilibrium problems, network flow problems and other areas [1]}, [2]}, [3]}. Despite the bad properties of the sum, such problems, both in convex and nonconvex cases, can be solved by full gradient or Newton methods with the efficiency typical for the good part of the objective [4]}, [5]}. However, for large-scale problems, which is also the case in this paper, the usual methods based on full gradient and Hessian computations are prohibitive. In this case, it appears that a reasonable approach to solve such problems is to use (block) coordinate descent methods.
